在無線通訊系統中，多重路徑干擾與非同步延遲與通道雜訊會導致訊號的損害。因此我們使用分集技術來降低訊號多重路徑衰減程度與通道雜訊的干擾。
本論文所使用的系統為非同步多載波直序分碼多工系統， 且在分集結合的技術中採用了最小均方差合併器。此合併器的設計與很多因素有關係包括展頻碼、通道衰減係數與使用者之間相對的延遲，它需要每個位元一個一個來計算。所以我們必須降低複雜度才會得到我們想要的最小均方差合併器。
在本論文中，我們採用降秩的方法。它是將接收信號投影到克里羅夫子空間上且去觀察投影於的子空間的信號，以推導出我們要的降秩最小均方差合併器。我們可以發現當降秩合併器在一個大系統中 (使用者數目與展頻增益趨近於無限大，且比值為一個定值) 會收斂成一個固定的濾波器。我們以此固定的濾波器當作分集合併器的近似值。所以我們就不需要在每一個位元重新計算合併器。在模擬結果中，我們發現近似合併器所導致的效能損失非常小。

In wireless communication, a signal is impaired by interference, multipath fading and channel noise. Diversity techniques can be used to reduce these impairments. In this thesis, an asynchronous multicarrier direct sequence code division multiple access (MC-DS-CDMA) system is addressed, and the minimum mean square error (MMSE) combiner is adopted as the diversity combining technique. As the combiner is dependent on a number of factors, including the spreading codes, channel fading coefficients, and relative delays among users, it needs to be computed from symbol to symbol. Therefore, it is desirable to have a reduced-complexity method for obtaining the combiner.

A reduced-rank approach is employed in this thesis. The received signal is projected to the Krylov subspace, and the projection on the subspace is used as the observation to obtain a reduced-rank MMSE combiner. It is found that this reduced-rank combiner converges to a deterministic filter in a large system. The deterministic combiner obtained in the large system assumption is used as the approximation for the combiner in a finite-size system. Thus, there is no need to re-compute the combiner at every symbol. From the simulation results, it is found that the performance loss due to this approximated combiner is negligible.

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